According to the Evening Standard, Khan has struck an outline agreement with FA boss Martin Glenn to transfer Wembley to foreign ownership for the first time.
Wembley, owned by England's soccer association and home to its national team, the FA Cup final and many of Britain's biggest sporting events, has staged regular NFL games for about a decade.
Khan won't relocate England national teams if Wembley bid is accepted
A spokesman for the FA confirmed on Thursday it had received an offer to buy the stadium and British media said the deal could be worth up to 1 billion pounds (around Rs 929 crore).
The deal would see Khan pay £500m up front to the FA and allow the federation keep Wembley hospitality business that is valued at around £300m.
"Having stadium options in London has always been critical to the National Football League and, in tandem with our 10-year partnership with Tottenham Hotspur, this new relationship would allow for even greater flexibility in scheduling future National Football League games in London".
Wembley, which has a 90,000-capacity, was reopened in 2007 after the FA's seven-year, £757 million rebuilds of the home of English football.
The money from the sale of Wembley would allow the governing body to reinvest in the English game's grassroots, particularly pitches, and stage more England games way from the capital, a plan to which it is already committed.
Khan added that the move is one that could solidify the Jags' position as the league's global franchise, which also helps their longevity in Jacksonville.
He said: "We are very happy for Shad Khan and the Jacksonville Jaguars". Over the past several years, it became clearer to us and the FA that the idea of our purchase of Wembley Stadium made a lot of sense for all of us.
"I think the signals of the Jaguars relocating to London are premature and very assumptive at this point", he told Reuters. "Wembley is a special place, beloved in London and known throughout the world".